GCF of 423/87, 282/1986
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 423/87, 282/1986 i.e 141/57594 easily. The following is the detailed procedure to determine the greatest common factor of fractions 423/87, 282/1986.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 423/87,282/1986?
Given fractions are 423/87,282/1986
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 423/87,282/1986, numerators are 423,282
Denominators are 87,1986
The GCF of 423,282 is 141 .
LCM of 87,1986 is 57594.
The greatest common factor of 423/87,282/1986 = [GCF of 423,282]/[LCM of 87,1986]= 141/57594
Therefore, the GCF of 423/87,282/1986 is 141/57594.
To find the highest common factor of 423,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 423 are 1, 3, 9, 47, 141, 423
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 423,282 is 141.
Lets's calculate GCF of 423,282
| 3 | 423, 282 |
| 47 | 141, 94 |
| 3, 2 |
∴ So the GCF of the given numbers is 3 x 47 = 141
Greatest Common Factor of 423,282 By Matching Biggest Common Factor Method
Now, list down the factors of 423
:1,3,9,47,141,423
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 423,282 . The biggest common factor number is the GCF number.
So the greatest common factor 423,282 is 141.
Lets's calculate LCM of 87,1986
| 3 | 87, 1986 |
| 29, 662 |
∴ So the LCM of the given numbers is 3 x 29 x 662 = 57594
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 141/57594
Therefore, the GCF of Fractions 423/87,282/1986 is 141/57594
Least Common Multiple of 87,1986 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 87,1986 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,1986) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(87,1986) x common factors =3 x 1 = 3
LCM(87,1986) = ( 87 × 1986 ) / 3
LCM(87,1986) = 172782 / 3
LCM(87,1986) = 57594
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FAQs on GCF of Fractions of 423/87, 282/1986
1. What is the HCF of 423,282?
The HCF of 423,282 is 141
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 423/87, 282/1986?
Answer: GCF of Numerators as per given numbers 423/87, 282/1986 is
GCF of Numerators i.e. for 423,282 is 141
LCM of denominators i.e. for 87,1986 is 57594.
Thus, GCF of Fractions is 141/57594.Finally, GCF of Fractions for 423/87, 282/1986 is 141/57594.